Two parallel wires conduct equal currents in the same direction. (a) At a point in the plane of the wires midway between them, do the individual fields of the wires cancel or reinforce each other? (b) At a point far away from the wires, do their individual fields tend to cancel or reinforce each other?
To determine whether the individual magnetic fields of the parallel wires cancel or reinforce each other, we can use the right-hand rule.
(a) At a point in the plane of the wires midway between them:
To find the direction of magnetic fields produced by each wire, use the right-hand rule. Point your right thumb in the direction of the current in one wire. Your curled fingers will then wrap around the wire, indicating the direction of the magnetic field it produces. Repeat the process for the other wire.
Since the wires are conducting equal currents in the same direction, the magnetic fields produced by the wires will have the same direction. Consequently, the magnetic fields generated by the wires will reinforce each other at the point midway between them. Hence, the individual fields will not cancel, but rather reinforce each other.
(b) At a point far away from the wires:
The strength of a magnetic field produced by a current-carrying wire decreases with distance. Hence, at a point far away from the wires, the magnetic fields generated by each wire will be weaker. Although they may not cancel each other completely, the distance between the wires and the point in consideration will significantly reduce their influence. Therefore, the individual fields tend to partially cancel each other and reduce in magnitude, resulting in a weaker net magnetic field.